few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Recognize and represent proportional relationships between quantities.
problem_activity: Activity
The purpose of this activity is for students to practice rewriting expressions representing percent change so that they only use multiplication.
Launch
Allow students to work with a partner or individually.
Student Facing
Write an equivalent expression using the distributive property:
\(65 - 0.45 \boldcdot 65\)
\(65 + 0.45 \boldcdot 65\)
\(91 \boldcdot (1.2)\)
\(x + 0.04x\)
Evaluate by multiplying just two numbers in your calculator. Write down the expression you calculated.
130 increased by 10%
25 decreased by 30%
50% more than 38
6% less than 200
Write an equivalent expression that only uses multiplication:
\(p - 0.35p\)
\(z - 0.85z\)
\(q + 0.06q\)
\(r + 0.64r\)
Student Response
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Activity Synthesis
Either display the correct solutions or invite students to share their solutions. Here are sample questions to promote discussion:
“Why is it okay to rewrite an expression like
\(z - 0.85z\)
so that it looks like
\(0.15z\)
?” (Use the distributive property, or think about how an amount decreased by 85% is the same as 15% of the amount.)
“Have you heard some examples of percent increase or decrease used in the real world? What were they?” (Sample response: The news might talk about crime decreasing by 10% compared to last year, or home prices in an area increasing by 25%.)
“How is an expression representing percent increase (like
\(1.05x\)
) different from an expression representing percent decrease (like
\(0.95x\)
)?” (The coefficient is greater than 1 versus less than 1. This is a result of adding or subtracting a percentage of the original amount.)


correct_option_index: 0